FarkasDual


FarkasDual

Type: double
Modifiable: No

Together, attributes FarkasDual and FarkasProof provide a certificate of the infeasibility of the given problem.

They are a solution to the following system:


\begin{displaymath}\bar{a}x = \lambda^tAx \leq \lambda^tb = -\beta + \sum\limits...
...{a}_j<0}\bar{a}_iU_j + \sum\limits_{i:\bar{a}_j>0}\bar{a}_jL_j,\end{displaymath}

where <span>$</span>L_j<span>$</span> is the lower bound of variable <span>$</span>x_j<span>$</span>, <span>$</span>U_j<span>$</span> is the upper bound of variable <span>$</span>x_j<span>$</span>, <span>$</span>\lambda_i \geq 0<span>$</span> if the <span>$</span>i<span>$</span>-th constraint has a <span>$</span>\leq<span>$</span> sense, <span>$</span>\lambda_i \leq 0<span>$</span> if the <span>$</span>i<span>$</span>-th constraint has a <span>$</span>\geq<span>$</span> sense, <span>$</span>\bar{a}_j \geq 0<span>$</span> if <span>$</span>U_j = \infty<span>$</span>, and <span>$</span>\bar{a}_j
\leq 0<span>$</span> if <span>$</span>L_j = -\infty<span>$</span>.

The FarkasProof correspond to <span>$</span>\beta<span>$</span>, and FarkasDual correspond to <span>$</span>\lambda<span>$</span> in the system above.

Note that any solution to the system above, with <span>$</span>\beta>0<span>$</span>, provides an infeasible constraint, <span>$</span>\bar{a}x\leq\lambda^tb<span>$</span>, derived from the set of original constraints and bounds. Also, the proof is independent of the objective function and of the model sense of the problem at hand.

This attribute is only available when parameter InfUnbdInfo is set to 1.

For examples of how to query or modify attributes, refer to our Attribute Examples.